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The Queen has called for national reconciliation in the wake of the Scottish referendum, urging her subjects to temper the “strong feelings and contrasting emotions” inspired by the campaign with a new spirit of mutual respect.

Buckingham Palace issued a statement on Friday in which the monarch – who was prohibited from taking sides in the debate – pledged her family’s support in healing divisions caused by the “strongly-held opinions” expressed during in the run-up to the poll.

Despite the No campaign’s comprehensive victory in the poll – winning 55 per cent of the vote against Yes’ 45 per cent – the result spells intense disappointment for the 1.6m Scots whose hopes of independence have been thwarted. The whole country now faces major constitutional upheaval and continued debate about the devolution of further powers to Scotland and the prospect of English MPs being given more control over their own affairs.

Amid continuing uncertainty, the Queen acknowledged the conflicts that had arisen between “family, friends and neighbours” and reflected that such discussions were part of the UK’s “robust democratic tradition”. Writing from her Balmoral residence in Aberdeenshire, she asked Britons to remember that “despite the range of views that have been expressed, we have in common an enduring love of Scotland, which is one of the things that helps to unite us all”.

“Knowing the people of Scotland as I do, I have no doubt that Scots, like others throughout the United Kingdom, are able to express strongly-held opinions before coming together again in a spirit of mutual respect and support, to work constructively for the future of Scotland and indeed all parts of this country,” her statement read.

Palace officials confirmed that the Queen had been following events closely, and her role as head of state in an independent Scotland was the focus of significant discussion and speculation during the campaign.

With fears growing earlier this month that the Yes vote was strengthening, the Queen met David Cameron in Scotland for crisis talks. As the poll approached the Queen even made an unexpected intervention urging Scots to “think very carefully” about the vote.

In her comments – made after a Sunday service at Crathie Kirk near the Balmoral estate – the monarch was careful not to endorse either side but told a small group outside the church: “Well, I hope people will think very carefully about the future.” It is unusual for the Queen to speak to well-wishers at the Sunday service.

However, this cautious move prompted outrage among antimonarchy campaigners. The Republic pressure group on Thursday called for a parliamentary inquiry into what it called “underhand, deliberate and provocative” interventions by the Sovereign, and said it would be writing to the Justice Secretary requesting a probe into the actions of the Queen and her advisers.

Graham Smith, the group’s chief executive, said: “We would normally expect a head of state to take an active interest in such a momentous referendum, but the deal with the monarchy is that the monarch stays quiet and keeps out of these debates.”

“The real problem is the system,” Mr Smith added. “But that doesn’t excuse the Queen making her views known in such an underhand way while having her press office insist she is impartial.”

Buckingham Palace has always insisted that the Queen believed the referendum was “a matter for the people of Scotland”.